Estimating the rms chemical potential in the puddle regime to be \(\epsilon _F\sim \hbar v_F \sqrt{\pi \tilde{n}}\)  , we expect a significant \(T\) -dependence of \(\sigma _{min}(T)\)  only for \(k_B T \gg \hbar v_f \sqrt{\pi \tilde{n}}\) . For unsuspended samples \(\tilde{n}\sim 10^{11}\)  cm\(^{-2}\)  [1]}, [2]} corresponding to \(T_F^*= \hbar v_f \sqrt{\pi \tilde{n}}/k_B \sim 400\)  K, which is used to explain why in "dirty" devices \(\sigma _{min}\)  lacks a significant \(T\) -dependence in the range [0, 300 K]. The weak \(T\) -dependence in suspended samples before current annealing implies a similar situation. In contrast, after current annealing \(\sigma _{min}(T)\)  shows \(T\) -dependence down to \(T\sim 10\)  K (Fig. 4) This implies an upper bound of \(\tilde{n}<10^8\)  cm\(^{-2}\) , consistent with fits to the density dependence of transport data [3]} and represents further evidence for the high quality of suspended graphene.
